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%I #33 Jan 13 2016 00:34:23
%S 2,7,2,2,6,8,7,7,7,6,8,5,8,8,5,7,6,4,6,7,0,7,9,4,5,8,0,5,1,4,9,4,4,5,
%T 8,2,8,7,4,8,9,8,0,1,5,8,7,7,8,6,8,3,6,0,1,0,7,2,4,0,8,6,9,4,3,6,1,9,
%U 3,3,4,9,7,6,2,6,2,3,1,3,7,2,1
%N Decimal expansion of exponential growth rate of number of labeled planar graphs on n vertices.
%H Gheorghe Coserea, <a href="/A266390/b266390.txt">Table of n, a(n) for n = 2..51000</a>
%H Omer Giménez, Marc Noy, <a href="http://dx.doi.org/10.1007/978-3-0348-7915-6_12">Estimating the Growth Constant of Labelled Planar Graphs</a>, Mathematics and Computer Science III, Part of the series Trends in Mathematics 2004, pp. 133-139.
%H Omer Gimenez, Marc Noy, <a href="http://dx.doi.org/10.1090/S0894-0347-08-00624-3">Asymptotic enumeration and limit laws of planar graphs</a>, J. Amer. Math. Soc. 22 (2009), 309-329.
%F Equals 1/R(A266389), where function t->R(t) is defined in the PARI code.
%F A066537(n) ~ A266391 * A266390^n * n^(-7/2) * n!.
%e 27.2268777685...
%o (PARI)
%o A266389= 0.6263716633;
%o A1(t) = log(1+t) * (3*t-1) * (1+t)^3 / (16*t^3);
%o A2(t) = log(1+2*t) * (1+3*t) * (1-t)^3 / (32*t^3);
%o A3(t) = (1-t) * (185*t^4 + 698*t^3 - 217*t^2 - 160*t + 6);
%o A4(t) = 64*t * (1+3*t)^2 * (3+t);
%o A(t) = A1(t) + A2(t) + A3(t) / A4(t);
%o R(t) = 1/16 * sqrt(1+3*t) * (1/t - 1)^3 * exp(A(t));
%o 1/R(A266389)
%Y Cf. A066537, A266389, A266391.
%K nonn,cons
%O 2,1
%A _Gheorghe Coserea_, Dec 28 2015
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